Good news, everyone. 
I got a query to work. I wrapped my original query in:
SELECT DISTINCT(user_id), CURRENT_TIMESTAMP granted_at
FROM (my existing query here) AS top_answerers
WHERE (:backfill OR ( user_id IN (:user_ids) ))
So in this case, the multiple user_ids was the issue. I guess users won’t be able to get this badge multiple times, but I can live with that for now.